And now for something completely different… or is it?

This problem comes from the ancient Greeks (Euclid, to be exact). Suppose you have a rectangle which is one unit tall and has this special property: if you cut off a square piece from the end of the rectangle, you’re left with a smaller rectangle that has the same proportions as the original rectangle. How long is the original rectangle?

Maybe this picture will help you see what is going on. Starting with the big blue rectangle at the top, the white square is cut off from the left side, leaving the smaller blue rectangle — which is just a smaller copy of the big blue rectangle.

E-mail me with questions, comments, or solutions, or post them here. Also, if anyone has solved either or both parts of Challenge #4, feel free to post your solution now!

This is just a golden rectangle, is it not?

bob: right you are!